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FOR THE MERINGUE: Adjust oven rack to middle position and heat oven to 250 degrees. Using ruler and pencil, draw 13 by 10 1/2-inch rectangle on piece of parchment paper. Grease baking sheet and place parchment on it, ink side down.
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Process almonds, hazelnuts, cornstarch, and salt in food processor until nuts are finely ground, 15 to 20 seconds. Add 1/2 cup sugar and pulse to combine, 1 to 2 pulses.
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Using stand mixer fitted with whisk, whip egg whites and cream of tartar on medium-low speed until foamy, about 1 minute. Increase speed to medium-high and whip whites to soft, billowy mounds, about 1 minute. With mixer running at medium-high speed, slowly add remaining 1/2 cup sugar and continue to whip until glossy, stiff peaks form, 2 to 3 minutes. Fold nut mixture into egg whites in 2 batches. With offset spatula, spread meringue evenly into 13 by 10 1/2-inch rectangle on parchment, using lines on parchment as guide. Using spray bottle, evenly mist surface of meringue with water until glistening. Bake for 1 1/2 hours. Turn off oven and allow meringue to cool in oven for 1 1/2 hours. (Do not open oven during baking and cooling.) Remove from oven and let cool to room temperature, about 10 minutes. (Cooled meringue can be kept at room temperature, tightly wrapped in plastic wrap, for up to 2 days.).
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FOR THE BUTTERCREAM: Heat milk in small saucepan over medium heat until just simmering. Meanwhile, whisk yolks, sugar, cornstarch, and salt in bowl until smooth. Remove milk from heat and, whisking constantly, add half of milk to yolk mixture to temper. Whisking constantly, return tempered yolk mixture to remaining milk in saucepan. Return saucepan to medium heat and cook, whisking constantly, until mixture is bubbling and thickens to consistency of warm pudding, 3 to 5 minutes. Transfer pastry cream to bowl. Cover and refrigerate until set, at least 2 hours or up to 24 hours. Before using, warm gently to room temperature in microwave at 50 percent power, stirring every 10 seconds.
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Stir together amaretto and espresso powder; set aside. Using stand mixer fitted with paddle, beat butter at medium speed until smooth and light, 3 to 4 minutes. Add pastry cream in 3 batches, beating for 30 seconds after each addition. Add amaretto mixture and continue to beat until light and fluffy, about 5 minutes longer, scraping down bowl thoroughly halfway through mixing.
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FOR THE GANACHE: Place chocolate in heatproof bowl. Bring cream and corn syrup to simmer in small saucepan over medium heat. Pour cream mixture over chocolate and let stand for 1 minute. Stir mixture until smooth. Set aside to cool until chocolate mounds slightly when dripped from spoon, about 5 minutes.
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Carefully invert meringue and peel off parchment. Reinvert meringue and place on cutting board. Using serrated knife and gentle, repeated scoring motion, trim edges of meringue to form 12 by 10-inch rectangle. Discard trimmings. With long side of rectangle parallel to counter, use ruler to mark both long edges of meringue at 3-inch intervals. Using serrated knife, score surface of meringue by drawing knife toward you from mark on top edge to corresponding mark on bottom edge. Repeat scoring until meringue is fully cut through. Repeat until you have four 10 by 3-inch rectangles. (If any meringues break during cutting, use them as middle layers.).
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Place 3 rectangles on wire rack set in rimmed baking sheet. Using offset spatula, spread 1/4 cup ganache evenly over surface of each meringue. Refrigerate until ganache is firm, about 15 minutes. Set aside remaining ganache.
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Using offset spatula, spread top of remaining rectangle with 1/2 cup buttercream; place on wire rack with ganache-coated meringues. Invert 1 ganache-coated meringue, place on top of buttercream, and press gently to level. Repeat, spreading meringue with 1/2 cup buttercream and topping with inverted ganache-coated meringue. Spread top with buttercream. Invert final ganache-coated strip on top of cake. Use 1 hand to steady top of cake and spread half of remaining buttercream to lightly coat sides of cake, then use remaining buttercream to coat top of cake. Smooth until cake resembles box. Refrigerate until buttercream is firm, about 2 hours. (Once buttercream is firm, assembled cake may be wrapped tightly in plastic and refrigerated for up to 2 days.).
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Warm remaining ganache in heatproof bowl set over barely simmering water, stirring occasionally, until mixture is very fluid but not hot. Keeping assembled cake on wire rack, pour ganache over top of cake. Using offset spatula, spread ganache in thin, even layer over top of cake, letting excess flow down sides. Spread ganache over sides in thin layer (top must be completely covered, but some small gaps on sides are OK).
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Garnish top of cake with hazelnuts. Holding bottom of cake with 1 hand, gently press almonds onto sides with other hand. Chill on wire rack, uncovered, for at least 3 hours or up to 12 hours. Transfer to platter. Cut into slices with sharp knife that has been dipped in hot water and wiped dry before each slice. Serve.
